Hayyim ben Menahem Algazi () was the rabbi of the island of Rhodes and Smyrna and author of "Bene Ḥayyai". He lived in the seventeenth century.
Algazi authored "Bene Ḥayyai" (Sons of My Life), containing notes and in the sequence of the Arba'ah Turim. It was edited by the author's pupil, Meir Danon, and published at Orthokoi (near Constantinople) in 1712. Appended to it are the author's "Chiddushim," miscellaneous notes on Shevu'ot, Sanhedrin, Gittin, etc., edited by Hayyim ben Isaac Raphael Alfandari.